My question is, what is the maximum number of LEDs I can use?I know this board has an over current protection of 500mA. http://arduino.cc/en/Main/ArduinoBoardDiecimilaDoes that mean I need to stay under 500mA?I probably only need 21 LEDs, but may need more,so to play it safe, no more than 24 of the LEDs (20mA x 24 = 480mA)?

500mA is only on the 5V line connected to the USB Port. If you are powering from a DC jack, the current limit is less obvious. It depends on how much heat the regulator generates, which will depend on the Input voltage.

At 9V, you can easily get over 500mA out of it.

Of course, you could also look at using the 9V raw on the LEDs, moving some of the power dissipation to the TLC instead of the Arduino's regulator. That might work better if you were putting more than 1 LED (in series) on each output.